Question

2 the following sentences describe a rhombus. fill the appropriate words in the blanks. (1) in a rhombus, since the four are all equal, the two pairs of sides of the rhombus are equal respectively. the quadrilateral in which the two pairs of opposite sides are equal respectively, confirms the property of a, so the rhombus is a parallelogram. (2) in rhombus abcd on the right, from ab = ad, bo = do and ao is shared, △abo ≅ △. from this fact, ∠aob = ∠aod = °. so, ac ⊥ is proved. therefore, the of the rhombus are shown to intersect perpendicularly.

Explanation:

(1)

Step1: Recall rhombus side properties

A rhombus has four equal sides. So the first blank is "sides".

Step2: Recall opposite sides in rhombus

In a rhombus, the two pairs of opposite sides are equal (since all four sides are equal, opposite sides are equal). So the second blank is "opposite".

Step3: Recall parallelogram property

A quadrilateral with two pairs of opposite sides equal is a parallelogram. So the third blank is "parallelogram".

(2)

Step1: Identify congruent triangle

Given \(AB = AD\), \(BO = DO\), and \(AO\) is common. By SSS (Side - Side - Side) congruence criterion, \(\triangle ABO\cong\triangle ADO\). So the first blank is "ADO".

Step2: Find angle measure

Since \(\triangle ABO\cong\triangle ADO\), \(\angle AOB=\angle AOD\). And \(\angle AOB+\angle AOD = 180^{\circ}\) (linear pair), so \(\angle AOB=\angle AOD = 90^{\circ}\). So the second blank is "90".

Step3: Identify perpendicular lines

From \(\angle AOB = 90^{\circ}\), we can say \(AC\perp BD\). So the third blank is "BD".

Step4: Recall rhombus diagonals property

The diagonals of a rhombus intersect perpendicularly. So the fourth blank is "diagonals".

Answer:

(1) First blank: sides; Second blank: opposite; Third blank: parallelogram.
(2) First blank: ADO; Second blank: 90; Third blank: BD; Fourth blank: diagonals.